Distance to simplicies

d, λ = distancetosimplex(y, x::NTuple{M,SVector{N, T}})

Get the distance d::T to the simplex spanned by M points x and barycentric coordinates λ::NTuple{N, T} of the projection of y.

d, t = distancetolinesegment(x, (a,b))

Compute distance of x to line segment (a,b).

Returns (d, t) with distance d and parameter 0 <= t <= 1 such that projection point is (1-t)*a + t*b.

t, r = projectontoline(x, (a, b))

Project x onto line (a, b). Returns (t, r) for Π(x) = a + t*r.

Π, t, r = projectontolinesegment(x, (a, b))

Project x onto line segment (a, b).

Returns (Π(x), t, r) for Π(x) = a + t*r, 0 <= t <= 1.

λ = barycentriccoordinates(x, (a,b,c)) # in 2d

Compute barycentric coordinates of x w.r.t. to planar triangle (a,b,c).

This function will always return finite barycentric coordinates, even if the triangle is degenerated.

d, λ = distancetotriangle(x, (a,b,c))
d, λ = distancetotriangle(::Val{2}, x, (a,b,c)) # in 2d
d, λ = distancetotriangle(::Val{3}, x, (a,b,c)) # in 3d

Compute distance of x to triangle (a,b,c).

Returns (d, λ) with distance d and barycentric coordinates λ.